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Pedagogies to improve learning Students need to trust their teacher to know them as people, know how to teach, and know what to teach As the teacher, I am the authority in the room, and from Day 1 I behave consistently, and differently

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Teacher as authority I am in charge, so I arrange the seating In alphabetical order Seldom changed, and only by me Cycle rows forward from time to time

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Pause I wait at least 10 seconds after posing a question before accepting an answer Why do you think I do this? Discuss briefly with the person next to you

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Re-frame the language I ban Miss, is it...? And give students alternative language to use (and reiterate it): I think it could be... It might be... I wonder if it could be... Were all allowed to make mistakes

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Random numbers Each student has a number on the roll and they write it down inside exercise book cover Alphabetical order means... Use this when I want to choose a student to answer – after pausing

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Random number expert I teach one (volunteer) student how to use their calculator to generate a random number from the class That student always generates random numbers when I want them

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My favourite questions What do you notice? What is the same and what is different?

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Work out what you can and see where it takes you I use this for geometry and trigonometry in particular

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Feedback from asking "What can I see?" to get started It helped me because it broke down the question step by step. It allowed me to think of the answer myself and find different strategies. Finding everything I could 'see' in the question made it easier when writing down my working to find the final answer.

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Kathleen Hart We need to build a bridge from the concrete to the abstract Bridge must be 2-way, must work both for doing and undoing Children's Understanding of Mathematics 11-16 (1981) Children's Understanding of Mathematics 11-16

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Do now! Every lesson starts with 3 – 5 questions hand-written on board Usually revision – previous lesson, previous year (simple), algebra skills Can take up to 15 minutes to do and process

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Homework These students need to learn that doing homework matters I set a little almost every day, students open book at start of lesson to show me HW while they complete the Do Now I record in my mark book whether reasonable attempt or not

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Feedback Not just ticks and crosses or N, A, M, E Always a sentence about what understanding student has shown, and what they need to do to progress. Talk about A and M: What level have we been working on?